Archive of changes made during 2008. The substantive content of this page should not be altered. For past versions of this page beyond its own history, start here and work backwards.
Toby (Dec 28): I added a bunch of stuff about apartness relations. (Most of it is probably even correct.) I tried to say as much as I could in terms of enriched category theory, but the topic is really analysis.
John (Dec 23): I expanded the entry on action groupoid and started one for action and automorphism. In the process I noted that Urs seems to be using for the category of sets, while most mathematicians use Set. We should settle (pardon the pun) this issue. I hope that someday there will be lots of entries on specific important categories, listing some of the special features of these categories.
Urs (Dec 22): started replying to a question Eric raised at General Discussion about the shape of cells used in higher categories. Created geometric shapes for higher structures with a discussion of the general idea and linked to globular set, simplicial set and cubical set from there. Still plenty of room to add details. Am planning to give details on the monoidal structure on cubical sets and the induced Crans-Gray tensor product on -categories.
Urs (Dec 20): I started to add alphabetical lists of all related entries to the big headline entries that are linked to from the sidebar of the HomePage. So far I did this in category theory, sheaf and topos theory, foundations and higher category theory. It might be good if each time we create a new entry we think about adding the correspondin link to one of these general lists.
Urs (Dec 20): I replied to the discussion at monoidal category on “Where does all this structure and coherence come from?” by adding a subsection on how all this comes from the general concept of -lax functor for which one formalization can be given in terms of orientals and Street’s descent. The pentagon identity is precisely the fourth oriental!
Toby (Dec 20–23): I won't do anything, since I'll be travelling. (Just in case you wonder where I am.)
John (Dec 20): I sketched the definitions of monoidal category, braided monoidal category, and symmetric monoidal category and gave links to full definitions and explanations. Is someone good enough at drawing diagrams in this environment to draw the necessary diagrams — e.g. pentagon and hexagon identity?
Urs: recently, after Eric had requested an “arrow-theoretic” description of category algebra and of graded vector spaces, I had provided a description in terms of bi-branes and remarked that this is part of a bigger picture. That bigger picture, together with these examples, is now described over in my private area at Nonabelian cocycles and their quantum symmetries. For completeness I have added links to that to category algebra and graded vector space. Instead of giving the impression of forcing this relation to my work upon these entries, I would like you to understand this as an invitation to check and, if necessary, criticize.